Brian Harkins, 45, was found at the door of his house in Westmuir Place, Rutherglen, around 10:10am on Wednesday.
He was pronounced dead at the scene. At least eight plain-clothed officers attended the scene alongside a forensic team.
Detectives said the shooting did not appear to have been a random attack.
A post-mortem examination was carried out yesterday and Strathclyde Police are now treating Mr Harkins’ death as murder.
Detective Chief Inspector Kenny Graham said: “A team of detectives has been assigned to this investigation and an incident room has been set up at Helen Street Police Office.
“Door-to-door inquiries are being carried out, CCTV footage is being gathered by officers and forensic examinations are continuing in an effort to gather any information that could be pertinent to this investigation.
“I am in no doubt that there are people in the local area who may have seen or heard something, who haven’t yet come forward.”
DCI Graham said although Mr Harkins’ house was located at a busy junction, someone may have unwittingly seen something vital to the inquiry.
He added: “This is not being treated as a random attack and I would stress that everything is being done to catch the person responsible.”